In the tabletop game Dungeon\'s & Dragons, players sometimes are allowed to roll
ID: 3073073 • Letter: I
Question
In the tabletop game Dungeon's & Dragons, players sometimes are allowed to roll two 20-sided dice to determine whether or not the action they are taking is a success. They are allowed to take the highest number between the two rolls and compare it to some threshold. Suppose that a player needs to roll a 14 or higher on at least one of the dice to succeed. What is their probability of success?
Put your answer in percentage form (e.g. 10.71 not 0.1071) and then round to two decimal places. Do not include a % sign.
Explanation / Answer
When a two sided die is rolled possible number of outcomes are 20.
Out of 20 outcomes 13 are less than 14 and 7 are greater than equal to 14.
That is when two 20 sided dice are rolled possible number of outcomes are 20*20 =400.
The number of outcomes with first die showing 14 or greater and second die less than 14:
First die can shows 14 or greater in 7 ways and second die can show less than 14 in 13 ways so possible number of outcomes with first die having 14 or greater and second less than 14 is 13 *7 = 91
Likewise possible number of outcomes with second die having 14 or greater and first less than 14 is 13 *7 = 91
The possible number of outcomes both die showing 14 or greater is: 7*7 =49
That is possible number of ways to roll a 14 or higher on at least one of the dice is:
91+91 +49 = 231
That is probability of success is
P(success) = 231 /400 = 0.5775
Answer: 57.75